The halide mineral Zharchikhite with the chemical formula AlF(OH)2 is studied using first-principles methods of density functional theory with the local functional VBH, generalized gradient functionals PBE, BLYP, PBEsol, with an empirical dispersion correction in the form of D3(BJ) PBE-D3, BLYP-D3, global hybrid functionals PBE0, B3LYP, PBEsol0, hybrid functionals with range separation HSE06, SC-BLYP. It is shown that all functionals overestimate O-H and underestimate O-H∙∙∙O distances. The best values are provided by SC-BLYP, B3LYP. The bulk modulus, determined from the Birch-Murnaghan equation of state, is 72.32 GPa. The axes compress unevenly and the fastest is the longest one with a modulus of 217.3 GPa. The linear compressibility modulus of the Al-F bond has a similar value and is twice as large for the Al-O bond. Under pressure, the lengths of H∙∙∙O hydrogen bonds decrease faster and, conversely, O-H bonds slowly increase. Also, at a rate of 0.289°/GPa, the monoclinic angle also increases with pressure. The spectra of infrared absorption and Raman scattering of light have been calculated, in which vibrations of Al-F and Al-O atoms were actived in the region up to 600 cm−1; above 700 cm−1 there are translational vibrations of O-H with a dominant contribution of H1 (Au symmetry) or H2 (Bu symmetry) and above 3200 cm−1 100 % hydrogen atoms. For them, with increasing pressure, the wave numbers decrease and the Grüneisen parameters change from −0.36 to −0.54. The large value of the derivative dν/dP can be used to solve the inverse problem - finding the pressure P from the known wave number ν(P).